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A family of derivative-free methods with high order of convergence and its application to nonsmooth equations

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A family of derivative-free methods with high order of convergence and its application to nonsmooth equations

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dc.contributor.author Cordero Barbero, Alicia es_ES
dc.contributor.author Hueso Pagoaga, José Luís es_ES
dc.contributor.author Martínez Molada, Eulalia es_ES
dc.contributor.author Torregrosa Sánchez, Juan Ramón es_ES
dc.date.accessioned 2013-04-11T09:44:18Z
dc.date.available 2013-04-11T09:44:18Z
dc.date.issued 2012
dc.identifier.issn 1085-3375
dc.identifier.uri http://hdl.handle.net/10251/27791
dc.description.abstract A family of derivative-free methods of seventh-order convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the iteration. The efficiency indices of the members of this family are equal to 1.6266. Also, numerical examples are used to show the performance of the presented methods, on smooth and nonsmooth equations, and to compare with other derivative-free methods, including some optimal fourth-order ones, in the sense of Kung-Traubs conjecture. Copyright 2012 Alicia Cordero et al. es_ES
dc.description.sponsorship The authors would like to thank the referees for their valuable comments and for their suggestions to improve the readability of the paper. This research was supported by Ministerio de Ciencia y Tecnologia MTM2011-28636-C02-02 and by Vicerrectorado de Investigacion, Universitat Politecnica de Valencia PAID-06-2010-2285. en_EN
dc.format.extent 15 es_ES
dc.language Inglés es_ES
dc.publisher Hindawi Publishing Corporation
dc.relation.ispartof Abstract and Applied Analysis es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title A family of derivative-free methods with high order of convergence and its application to nonsmooth equations es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1155/2012/836901
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//MTM2011-28636-C02-02/ES/DISEÑO Y ANALISIS DE METODOS EFICIENTES DE RESOLUCION DE ECUACIONES Y SISTEMAS NO LINEALES/
dc.relation.projectID info:eu-repo/grantAgreement/UPV//PAID-06-2010-2285/
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Cordero Barbero, A.; Hueso Pagoaga, JL.; Martínez Molada, E.; Torregrosa Sánchez, JR. (2012). A family of derivative-free methods with high order of convergence and its application to nonsmooth equations. Abstract and Applied Analysis. 2012:1-15. https://doi.org/10.1155/2012/836901 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1155/2012/836901
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 15 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 2012 es_ES
dc.relation.senia 233919
dc.contributor.funder Universitat Politècnica de València
dc.contributor.funder Ministerio de Ciencia e Innovación es_ES
dc.description.references Kung, H. T., & Traub, J. F. (1974). Optimal Order of One-Point and Multipoint Iteration. Journal of the ACM, 21(4), 643-651. doi:10.1145/321850.321860 es_ES
dc.description.references Liu, Z., Zheng, Q., & Zhao, P. (2010). A variant of Steffensen’s method of fourth-order convergence and its applications. Applied Mathematics and Computation, 216(7), 1978-1983. doi:10.1016/j.amc.2010.03.028 es_ES
dc.description.references Dehghan, M., & Hajarian, M. (2010). Some derivative free quadratic and cubic convergence iterative formulas for solving nonlinear equations. Computational & Applied Mathematics, 29(1). doi:10.1590/s1807-03022010000100002 es_ES
dc.description.references Cordero, A., & Torregrosa, J. R. (2011). A class of Steffensen type methods with optimal order of convergence. Applied Mathematics and Computation, 217(19), 7653-7659. doi:10.1016/j.amc.2011.02.067 es_ES
dc.description.references Amat, S., & Busquier, S. (2006). On a Steffensen’s type method and its behavior for semismooth equations. Applied Mathematics and Computation, 177(2), 819-823. doi:10.1016/j.amc.2005.11.032 es_ES
dc.description.references Cordero, A., Hueso, J. L., Martínez, E., & Torregrosa, J. R. (2009). A modified Newton-Jarratt’s composition. Numerical Algorithms, 55(1), 87-99. doi:10.1007/s11075-009-9359-z es_ES
dc.description.references Cordero, A., & Torregrosa, J. R. (2007). Variants of Newton’s Method using fifth-order quadrature formulas. Applied Mathematics and Computation, 190(1), 686-698. doi:10.1016/j.amc.2007.01.062 es_ES
dc.description.references Amat, S., & Busquier, S. (2003). On a higher order Secant method. Applied Mathematics and Computation, 141(2-3), 321-329. doi:10.1016/s0096-3003(02)00257-6 es_ES


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